Fault detection in a mixed H2/H∞ setting

In this paper, we study the problem of fault detection in linear time-invariant systems, which contain two types of inputs: inputs with fixed and known spectral densities and inputs with bounded power. It is shown that this problem can be formulated as a mixed H₂/H_∞ filtering problem where the filter gain is computed by solving a pair of coupled Riccati equations. Alternatively, it is shown that the filter gain may be computed by transforming the problem into a convex optimization problem with a set of linear matrix inequality (LMI) constraints. The application of our results is illustrated by an example.